Empirical Formula for Neutron Yield for (α,n) Reactions from 63cu and 65cu Maher Nasir Sarsam Department of Engineering computing Technologies, College of Al- Salam University Bashair Mohammed Saied Aeshah Ali Hussein Department of Physic/ College of Education for Pure Science(Ibn Al-Haitham), University of Baghdad Inaam Noori Ibrahim Ministry of Education Received in 9 July 2013, Accepted in 10 October 2013 Abstract The calculated neutron yields from (α, n) reactions are very important in analyzing radiation shielding of spent fuel storage, transport and safe handling. The cross sections of 63Cu (α, n) 66Ga and 65Cu (α, n) 68Ga reactions are calculated for different α-energies using different sets of programs using Matlab language. The values deduced energy is from threshold to Eα= 30 MeV and to Eα= 40 MeV for 63Cu (α, n) 66Ga and 65Cu (α, n) 68Ga respectively. The weight average cross section was then used to calculate the neutron yields y0 (n/106α) for each reaction .The empirical formula was then suggested to calculate total neutron yield to each isotope. Keywords: Neutron yield, Cross section ,Empirical formula. 95 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 Introduction The nuclear data on (α,n) reactions play an important role in the fields of radiation shielding and critically safety relating to storage,transport and handling of spent fuel [1],as well as for the design and operation of a nuclear fuel cycle facility and particle accelerator facility [2]. The cross section for 63Cu (α, n) 66Ga has been measured for Eα= (7.8- 46) MeV by Levkovskij. (1991) [3] and the cross section for 63Cu (α, n) 66Ga reaction has been measured for (8-37) MeV by Zhukova at. et al [4] and for (7.8-42.5) MeV by Bryant at .et al [5] and for (8-40) MeV by Porile and Morrison [6] and for (8-38) MeV by Zweit at .et al [7] and for (8-38) MeV by Singh at .et al [8] . The cross section for65Cu (α, n) 68Ga reaction has been measured for Eα= (9- 45) MeV by Bhardwai [9] , and measured for (7.8- 46) MeV by Levkovskij. (1991) [3], and for (7.8- 46) MeV by Bryant at. et al [5], and for (7.8- 40) MeV by Porile at. et al [6], and for (7.8- 41.7) MeV by Bonesso. et al [10], and for (8.9- 40) MeV by Singh at. et al [8], and for (8.5-36.3) MeV by Szelecsenyi. et al [11]. In JENDL the total cross section and neutron yield for these reactions have been presented [12 ].The cross sections evaluations for (α,n) reactions for63Cu and65Cu target elements are calculated according to the available international atomic energy agency (IAEA) libraries and other experimental published data[12]. The stopping power depends on the type and energy of the incident particle and on the properties of the materials it passes. In passing through matter ,fast charged particles ionize the atoms or molecules which they inter. The yield for a target having any thickness can be defined as the ratio of the number of nuclei formed in the nuclear reaction to the number of particles incident on the target. Thick target yield is defined for a fixed macroscopic energy loss ,Ein -Eth, in a thick target. Integral yield is defined for a finite energy loss down to the threshold of the reaction ,Ein-Eth .The recommended cross sections discussed in the present work and the target stopping powers of SRIM program 2003 [SRIM 2003] were used to calculate the alpha yield for a target of significant thickness . Data Reduction and Analysis The Q-values and threshold energies of these reactions were calculated by using the atomic mass obtained from the following equations [13] : Q=931.5 [Mα +Mx - Mn-My]…………..(1) Eth=-Q [1+Mα/Mx]…………………… (2) Where Mn represents the mass of neutron and Mα,Mx and My are the atomic mass (in amu ) of 4He ,target and product nucleus respectively. The cross section data of 63Cu(α,n) 66Ga were published by [ 3-8] and of 65Cu(α,n) 68Ga were published by [3,5-6,8-10]. These data are plotted, interpolated and recalculated in steps of 1 MeV from threshold to 30 MeV for 63Cu and from 9 to 40 MeV for 65Cu by using different sets of programs using matlab language to obtain weighted average values for each reaction. *The normalization for the statistical distribution of cross sections errors to the corresponding cross section values for each another has been done . *The interpolation for the nearest data for each energy interval as a function of cross sections and their corresponding errors have been done using matlab program. *The interpolation values were calculated to obtain the adopted cross section which is based on the weighted average calculation according to the following expressions [13] : 𝜎𝑤.𝑎.= ∑ 𝜎𝑖 (∆𝜎𝑖) 2 𝑛 𝑖=1 ∑ 1 (∆𝜎𝑖) 2 𝑛 𝑖=1 …………………………… (3) Where the standard deviation error is 96 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 𝑆. 𝐷= 1 �∑ 1 (∆𝜎𝑖) 2 𝑛 𝑖=1 ………………………….(4) Where 𝜎𝑖 is the cross section value, ∆𝜎𝑖 is the corresponding error for each cross section value. Neutron Yields For an accelerating beam trans versing a target ,the occurred nuclear reactions produce N light particles per unit time and is given by [13] : 𝑌 = 𝐼𝑂 𝑁 𝑑 𝜎𝑥 … … … … . . … … (5) Experimentally the yield of neutrons detected per incident particle 𝑌𝑛 for an ideal ,thin and uniform target and mon energetic beam of energy E is given by [13] : 𝑌𝑛 = (𝑁𝑑𝑥)𝜎(𝐸𝑏)𝜂(𝐸𝑏) … … …. (6) Where 𝑁𝑑𝑥 is the areal number density of target atom and 𝜂 is the neutron –detection efficiency for a target which is not infinitesimally thin, the beam loses energy as it passes through the target and the yield is then given by [14]: 𝑌𝑛 = ∫ 𝜎(�́�)𝜂(�́�)𝑓𝑑�́� −𝑑𝐸 𝑑𝑋 (�́�) 𝐸𝑏 𝐸𝑡 … ………….(7) Where Et is (𝐸𝑏 − ∆𝐸) where E∆ is the energy loss of the beam in the target, f is the number of target atoms in each molecule, and 𝑑𝐸 𝑑𝑋 (�́�)is the stopping power per target molecule, if the target is sufficiently thick, and there exists one atom per each molecule (i.e.f=1) and taking 𝜂(𝐸) = 1 ,then the resulting yield is called the thick –target yield which is given by [15]: 𝑌(𝐸𝑏)=∫ 𝜎(𝐸)𝑑𝐸 𝑑𝐸 𝑑𝑋 𝐸𝑏 𝐸𝑡ℎ𝑟 ……………………(8) Where 𝐸𝑡ℎ𝑟 is the reaction threshold energy. Thus by measuring the yield at two closely spaced energies E1 &E2,one can determine the average value of the integrand over this energy interval as follows [15]: [ 𝜎(𝐸) 𝑑𝐸 𝑑𝑋 ]𝐸𝑏 = 𝑌(𝐸2) − 𝑌(𝐸1) 𝐸2 − 𝐸1 … … … … … … … … . . (9) Where 𝐸𝑏 is the average of E1 &E2,if 𝜎(𝐸) is the cross section which is available in the literature as a function of projectile energy 𝐸𝑏 for natural elements, then the neutron yield can be calculated using equation (9) Results and Discussion A-Cross Section Calculation The Q-value and threshold energies for 63Cu(α,n) 66Ga and 65Cu(α,n) 68Ga are presented in the table (1). The adopted value of cross section which is calculated in the present work are presented in the figures (1,2) from threshold to Eα=30 MeV and to Eα=40 97 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 MeV for 63Cu(α,n) 66Ga and 65Cu(α,n) 68Ga respectively. In each figure, the cross sections are compared with those deduced from the previous measurements. B-Yield calculation Neutron yields for 63Cu(α,n) 66Ga and 65Cu(α,n) 68Ga reactions calculated from reproduced cross section refs. [3-8], and [3,5-6,8-10] are presented in figures (3,4) together with the calculated weighted averages. The results obtained are consistent with each other. The neutron yields calculated in the present work have been considered as adopted neutron yield values by using the adopted neutron yields as an input data ,a matlab computer program have been executed to obtain the fitting parameters A& B for the power which fits formula equations For 63Cu(α,n) 66Ga reaction is: f(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2) + a3*exp(-((x-b3)/c3)^2) + a4*exp(- ((x-b4)/c4)^2) + a5*exp(-((x-b5)/c5)^2) + a6*exp(-((x-b6)/c6)^2)………………(10) a1 = 70.51 b1 = 31.18 c1 = 1.435 a2 = -403.3 b2 = 28.16 c2 = 3.197 a3 = -918.5 b3 = 24.83 c3 = 3.953 a4 = -55.09 b4 = 21.07 c4 = 2.537 a5 = 1879 b5 = 26.03 c5 = 6.429 a6 = 120.3 b6 = 15.81 c6 = 4.015 And for 65Cu(α,n) 68Ga reaction is: F(x) = a1*exp(-((x-b1)/c1).^2) + a2*exp(-((x-b2)/c2).^2) + a3*exp(-((x-b3)/c3).^2) + a4*exp(-((x-b4)/c4).^2)…………(11) a1 = 4547 b1 = 21.55 c1 = 5.059 a2 = -4067 b2 = 21.57 c2 = 4.947 a3 = 843.9 b3 = 31.69 c3 = 8.037 a4 = 48.48 b4 = 14.23 c4 = 3.291 98 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 Conclusions In the present work, the more recent cross section of (α,n) reactions for intermediate nuclei are reproduced and used to calculate the neutron yields at different α-particle energies .The obtained n-yields have been formalized using fitting procedure, as well as empirical formula has been established which combines the variation of n-yields with projectile kinetic energy and target atomic . References 1. Yamamuro,N. and Matsunobu,H., (2002) , Evaluation of the nuclear data on( α,n) reaction for F,Na,Al,Cr,Fe,NiandCu,Nucl.Sci.and Technol,1(2):188-191. 2. Murata,T. and Shibata,K. ,(2002), Evaluation of the (α,n) Reaction Nuclear Data for Light Nuclides,Nucl.Sci and Technol,1(2):76-79. 3. Levkovskij,V. N.(1991), Activation cross section nuclides of average masses (A=40-100) by protons and alpha-particles with average energies (E=10-50 MeV),Book: Levkovskij, Moscow. 4. Zhukova,O. A.;Kanashevich,V. I.;Laptev,S. V. and Chursin,G. P. , (1970),Excitation functions of reactions induced by alpha particles with maximum energy of 38 MeV on copper isotopes, J,IZK,4:1-8. 5. Bryant, E.A.; Cochran,D.R.F. and Knight, J.D., (1963) ,Excitation functions of reactions of 7 to 24 MeV 3He ions with 63Cu and 65Cu, J, PR, 130:1512. 6. Porile,N. T. and Morrison,D. L., (1959),Reactions of 63Cu and 65Cu with alpha particles, J,PR, 116:1193-1200. 7. Zweit,J.; Sharma,H.and Downey,S.,(1987),Production of gallium-66 ,a short lived positron emitting radio nuclide,J,ARI,38:499-501. 8. Singh,B. P.;Manoj; Sharma, K.;Musthafa, M. M.;Bhardwaj,H. D. and Prasad,R.,(2006), A study of pre-equilibrium emission in some proton and alpha –induced reactions, J,NIM/A, 562: 717. 9 .Bhardwai,H.D.;Gautam, A.K. and Prasad,R., (1988),Measurement and analysis of excitation functions for alpha-induced reactions e in copper, Journal Pramana, 31:109. 10. Bonesso ,O.; Ozafran, M. J.; Mosca, H. O.; Vazquez, M. E.;Capurro ,O. A. and Nassiff ,S. J., (1991),Study of pre-equilibrium effects on α-induced reactions on copper, Journal of Radio analytical and Nuclear Chemistry, 152(1): 189-197. 11. Szelecsenyi,F.; Kovacs, Z. and Nagatsu,K., (2012), Investigation of direct production of 68Ga with low energy multi particle accelerator, J,RCA, 100:5. 12. "JENDL (Japanese Evaluated Nuclear Data Library Version 3 Revision-3, (2002),J. Nucl. Sci. Technol, 39(11):1125-1136. 13. Audi,G. and Wapstra,A.H.,(1995),The1995update to the atomic mass evaluation,Nucl phys. A 595:409-480. 14. Wrean,P.R.(1998) ph.D thesis, California Institute of technology U.S.A. 15 Norman,E.B.;Chypp,T.E.;Lesko,K.T.;Grant,P.J.andWoodruff,G.L.,(1984),22Na production cross sections from the 19F(α,n) reaction,phys.Rev C,30( 4):1 339-1340. Table No.(1):Q-values and threshold energies for (α,n) reactions with 63Cu , 65Cu Reaction Threshold energy (MeV) Q-value(MeV) 63Cu(α,n) 66Ga 8.16±0.03 -7.513±0.032 65Cu(α,n) 68Ga 6.16±0.04 -5.843±0.12 99 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 Figure No .(1) : Cross sections of 63Cu (α, n) 66Ga reaction Figure No.(2) : Cross sections of 65Cu (α, n) 68Ga reaction 100 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 Figure No.(3) : Total Neutron yield of 63Cu (α, n) 66Ga reaction 101 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014 Figure No.(4) : Total Neutron yield of 65Cu (α, n) 68Ga reaction 63cuالصیغة التجریبیة للحصیلة النیوترونیة لتفاعالت (ألفا،نیوترون) من 65cuو ماھر ناصر سرسم الحاسبات ، كلیة السالم الجامعةقسم ھندسة تقنیات بشائر محمد سعید عائشة علي حسین قسم الفیزیاء ،كلیة التربیة للعلوم الصرفة ابن الھیثم ،جامعة بغداد. انعام نوري ابراھیم وزارة التربیة 2013تشرین االول 10البحث ، قبل 2013حزیران 9 استلم البحث الخالصة مھمة جدا في تحلیل االشعاع الناتج من تدریع للوقود المستنفذ (α, n)النیوترونیة لتفاعالتان حسابات الحصیلة عند 65Cu (α, n) 68Gaو 63Cu (α, n) 66Gaالمقاطع العرضیة لتفاعالتحسبت وتخزینھ ونقلھ والمعاملة اآلمنة لھ . طاقات الفـــــــــــــا المختلفة باستعمال مجموعة برامج بلغة ماتالب ، وقد تم االخذ بعین االعتبار طاقات الفا من طاقة على التوالي ، واستخدمت ھذه 65Cu (α, n) 68Gaو 63Cu (α, n)66Gaلتفاعل 40MeVوالى MeV 30 العتبة الى (نیوترون/ملیون الفا) لكل تفاعل ، بعد ذلك اقترحت y0الحصیلة النیوترونیة القیم للمقاطع العرضیة الموزونة في حساب الصیغة التجریبیة لحساب حصیلة النیوترون الكلیة في كال النظیرین . الحصیلة النیوترونیة ، المقطع العرضي ،الصیغة التجریبیة .:الكلمات المفتاحیة 102 | Physics @a@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ÚÓ‘Ój�n€a@Î@Úœäñ€a@‚Ï‹»‹€@·rÓ:a@Âig@Ú‹©@Ü‹127@@ÖÜ»€a@I2@‚b«@H2014 Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (2) 2014